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Theorem con34b 285
Description: Contraposition. Theorem *4.1 of [WhiteheadRussell] p. 116. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
con34b  |-  ( (
ph  ->  ps )  <->  ( -.  ps  ->  -.  ph ) )

Proof of Theorem con34b
StepHypRef Expression
1 con3 128 . 2  |-  ( (
ph  ->  ps )  -> 
( -.  ps  ->  -. 
ph ) )
2 ax-3 9 . 2  |-  ( ( -.  ps  ->  -.  ph )  ->  ( ph  ->  ps ) )
31, 2impbii 182 1  |-  ( (
ph  ->  ps )  <->  ( -.  ps  ->  -.  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6    <-> wb 178
This theorem is referenced by:  mtt  331  pm4.14  564  dfom2  4630  weniso  5786  dfsup2  7163  wemapso2lem  7233  pwfseqlem3  8250  indstr  10254  rpnnen2  12466  algcvgblem  12709  isirred2  15445  isdomn2  16002  ist0-3  17035  mdegleb  19412  dchrelbas4  20444  ltl4ev  24358  supnuf  24996  supexr  24998  raldifsni  26120  isdomn3  26890  conss34  27013
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179
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